M de Leeuw
We discuss the relation between the recently derived bound state S-matrices for the AdS5 x S5 superstring and Yangian symmetry. We will study the relation between this Yangian symmetry and the Bethe ansatz. In particular we can use it to derive the Bethe equations for bound states.
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We construct infinite number of conserved nonlocal charges for type IIB superstring on the AdS5xS5 space in the conformal gauge without assuming any kappa gauge fixing, and show that they satisfy the super Yangian algebra. The resultant algebra is the same as our previous work, where a special gauge was assumed in such a way that the Noether current satisfies a flatness condition. However the flatness condition for the Noether current of a superstring on the AdS space is broken in general. We show that the anomalous contribution is absorbed into the current where fermionic constraints play an …
We show that the recently found S-matrices describing the scattering of two-particle bound states of the light-cone string sigma model on AdS5 x S5 are compatible with Yangian symmetry. In case the invariance with respect to the centrally extended su(2|2) algebra is not sufficient to fully specify the scattering matrix, the requirement of Yangian symmetry provides an alternative to the Yang-Baxter equation and leads to a complete, up to an overall phase, determination of the S-matrix. We then compare the semi-classical limit of the bound state S-matrices with the universal classical r-matrix b…
We discuss a classical integrability in the type IIB string theory on the AdS_5 x S^5 background. By using the Roiban-Siegel formulation of the superstring on the AdS_5 x S^5, we carefully treat the Wess-Zumino term and the constraint conditions intrinsic to the supersymmetric case, and construct explicitly non-local charges for a hidden infinite-dimensional symmetry. The existence of the symmetry is shown by Bena-Polchinski-Roiban. Then the super Yangian algebra is calculated. We also show the Serre relation ensuring the structure of the Hopf algebra. In addition, the classical integrability …
We study the analytic Bethe ansatz in solvable vertex models associated with the Yangian $Y(X_r)$ or its quantum affine analogue $U_q(X^{(1)}_r)$ for $X_r = B_r, C_r$ and $D_r$. Eigenvalue formulas are proposed for the transfer matrices related to all the fundamental representations of $Y(X_r)$. Under the Bethe ansatz equation, we explicitly prove that they are pole-free, a crucial property in the ansatz. Conjectures are also given on higher representation cases by applying the $T$-system, the transfer matrix functional relations proposed recently. The eigenvalues are neatly described in terms…
In these notes we study integrable structure of conformal field theory by means of Liouville reflection operator/Maulik-Okounkov $R$-matrix. We discuss the relation between $RLL$ and current realization of the affine Yangian of $\mathfrak{gl}(1)$. We construct the family of commuting transfer matrices related to the Intermediate Long Wave hierarchy and derive Bethe ansatz equations for their spectra discovered by Nekrasov and Okounkov and independently by one of the authors. Our derivation mostly follows the one by Feigin, Jimbo, Miwa and Mukhin, but is adapted to the conformal case.
Integrability is believed to underlie the AdS3/CFT2 correspondence with sixteen supercharges. We elucidate the role of massless modes within this integrable framework. Firstly, we find the dressing factors that enter the massless and mixed-mass worldsheet S matrix. Secondly, we derive a set of all-loop Bethe Equations for the closed strings, determine their symmetries and weak-coupling limit. Thirdly, we investigate the underlying Yangian symmetry in the massless sector and show that it fits into the general framework of Yangian integrability. In addition, we compare our S matrix in the near-r…
In these notes we study integrable structures of conformal field theory with $\textrm{BCD}$ symmetry. We realise these integrable structures as affine Yangian $\mathfrak{gl}(1)$ "spin chains" with boundaries. We provide three solutions of Sklyanin $\textrm{KRKR}$ equation compatible with affine Yangian $R$-matrix and derive Bethe ansatz equations for the spectrum.
We study Bethe vectors of integrable models based on the super-Yangian $Y(\mathfrak{gl}(m|n))$. Starting from the super-trace formula, we exhibit recursion relations for these vectors in the case of $Y(\mathfrak{gl}(2|1))$ and $Y(\mathfrak{gl}(1|2))$. These recursion relations allow to get explicit expressions for the Bethe vectors. Using an antimorphism of the super-Yangian $Y(\mathfrak{gl}(m|n))$, we also construct a super-trace formula for dual Bethe vectors, and, for $Y(\mathfrak{gl}(2|1))$ and $Y(\mathfrak{gl}(1|2))$ super-Yangians, show recursion relations for them. Again, the latter all…
Yangian Doubles and off-Shell Bethe Vectors
通过经典系列的 Yangian 对偶的流构造了通用 $\fg$ 不变可积模型的离壳 Bethe 向量，并证明了它们满足定义性质，这些性质用于证明矩形递推关系并验证 $\ggo$ 不变可积模型中壳上 Bethe 向量的本征值性质。
We present a nested algebraic Bethe ansatz for a one dimensional open spin chain whose boundary quantum spaces are irreducible $\mathfrak{so}_{2n}$- or $\mathfrak{sp}_{2n}$-representations and the monodromy matrix satisfies the defining relations of the Olshanskii twisted Yangian $Y^\pm(\mathfrak{gl}_{2n})$. We use a generalization of the Bethe ansatz introduced by De Vega and Karowski which allows us to relate the spectral problem of a $\mathfrak{so}_{2n}$- or $\mathfrak{sp}_{2n}$-symmetric open spin chain to that of a $\mathfrak{gl}_{n}$-symmetric periodic spin chain. We explicitly derive th…
We establish features of so-called Yangian secret symmetries for AdS3 type IIB superstring backgrounds thus verifying the persistence of such symmetries to this new instance of the AdS/CFT correspondence. Specifically, we find two a priori different classes of secret symmetry generators. One class of generators, anticipated from the previous literature, is more naturally embedded in the algebra governing the integrable scattering problem. The other class of generators is more elusive, and somewhat closer in its form to its higher-dimensional AdS5 counterpart. All of these symmetries respect le…
We perform a detailed test of the quantum integrability of the AdS_5 x S^5 superstring in uniform light-cone gauge in its near plane-wave limit. For this we establish the form of the general nested light-cone Bethe equations for the quantum string from the long range psu(2,2|4) Bethe equations of Beisert and Staudacher. Moreover the scheme for translating excited string states into Bethe root excitations is given. We then confront the direct perturbative diagonalization of the light-cone string Hamiltonian in the near plane-wave limit with the energy spectrum obtained from the general nested l…
We find the Yangian symmetry underlying the integrability of type IIB superstrings on $AdS_3 \times S^3 \times S^3 \times S^1$ with mixed Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz flux. The abstract commutation relations of the Yangian are formulated via RTT realisation, while its matrix realisation is in an evaluation representation depending on the quantised coefficient of the Wess-Zumino term. The construction naturally encodes a secret symmetry of the worldsheet scattering matrix whose generators map different Yangian levels to each other. We show that in the large effective string ten…
The labelling of states of irreducible representations of GL(3) in an O(3) basis is well known to require the addition of a single O(3)-invariant operator, to the standard diagonalisable set of Casimir operators in the subgroup chain GL(3) - O(3) - O(2). Moreover, this `missing label' operator must be a function of the two independent cubic and quartic invariants which can be constructed in terms of the angular momentum vector and the quadrupole tensor. It is pointed out that there is a unique (in a well-defined sense) combination of these which belongs to the O(3) invariant Bethe subalgebra o…
We use the uniform light-cone gauge to derive an exact gauge-fixed Lagrangian and light-cone Hamiltonian for the Green-Schwarz superstring in AdS5xS5. We then quantize the theory perturbatively in the near plane-wave limit, and compute the leading 1/J correction to a generic string state from the rank-1 subsectors. These investigations enable us to propose a new set of light-cone Bethe equations for the quantum string. The equations have a simple form and yield the correct spinning string and flat space limits. Finally, we clarify the notion of closed sectors in string theory by proving the ex…
We reformulate the nested coordinate Bethe ansatz in terms of coproducts of Yangian symmetry generators. This allows us to derive the nested Bethe equations for the bound state string S-matrices. We find that they coincide with the Bethe equations obtained from a fusion procedure. The bound state number dependence in the Bethe equations appears through the parameters x^{\pm} and the dressing phase only.
Bethe vectors and recurrence relations for twisted Yangian based models
本文用代数 Bethe ansatz 研究 Olshanski 扭曲 Yangian 开放自旋链的奇情形，显式构造 Bethe 向量并利用复合模型方法导出偶、奇两种情形下的递推关系。
We consider the sl(N) twisted Yangian quantum spin chain. In particular, we study the bulk and boundary scattering of the model via the solution of the Bethe ansatz equations in the thermodynamic limit. Local defects are also implemented in the model and the associated transmission amplitudes are derived through the relevant Bethe ansatz equations.
We present the `Heisenberg picture' of the reflection algebra by explicitly constructing the boundary Yangian symmetry of an AdS/CFT superstring which ends on a boundary with non-trivial degrees of freedom and which preserves the full bulk Lie symmetry algebra. We also consider the spectrum of bulk and boundary states and some automorphisms of the underlying algebras.
In this paper we derive the universal R-matrix for the Yangian Y(u(2|2)), which is an abstract algebraic object leading to rational solutions of the Yang-Baxter equation on representations. We find that on the fundamental representation the universal R-matrix reduces to the standard rational R-matrix R = R_0(1 + P/u), where the scalar prefactor is surprisingly simple compared to prefactors one finds e.g. for sl(n) R-matrices. This leads precisely to the S-matrix giving the Bethe Ansatz of one-loop N = 4 Super Yang-Mills theory and two-loop N = 6 Chern-Simons theory.
We propose that Baxter's Z-invariant six-vertex model at the rational gl(2) point on a planar but in general not rectangular lattice provides a way to study Yangian invariants. These are identified with eigenfunctions of certain monodromies of an auxiliary inhomogeneous spin chain. As a consequence they are special solutions to the eigenvalue problem of the associated transfer matrix. Excitingly, this allows to construct them using Bethe ansatz techniques. Conceptually, our construction generalizes to general (super) Lie algebras and general representations. Here we present the explicit form o…
Two distinct $η$-deformations of strings on AdS$_5\times$S$^5$ can be defined; both amount to integrable quantum deformations of the string non-linear sigma model, but only one is itself a superstring background. In this paper we compare their conjectured all-loop worldsheet S matrices and derive the corresponding Bethe equations. We find that, while the S matrices are apparently different, they lead to the same Bethe equations. Moreover, in either case the eigenvalues of the transfer matrix, which encode the conserved charges of each system, also coincide. We conclude that the integrable stru…
We introduce fusion $U_q(G^{(1)}_2)$ vertex models related to fundamental representations. The eigenvalues of their row to row transfer matrices are derived through analytic Bethe ans{ä}tze. By combining these results with our previous studies on functional relations among transfer matrices(the $T$-system), we conjecture explicit eigenvalues for a wide class of fusion models. These results can be neatly expressed in terms of a Yangian analogue of the Young tableaux.
We study the highest states in the compact rank-1 sectors of the AdS5 X S5 superstring in the framework of the recently proposed light cone Bethe Ansatz equations. In the su(1|1) sector we present strong coupling expansions in the two limits L,lambda -> OO (expanding in power of lambda^{-1/4} with fixed large L) and lambda, L -> OO (expanding in power of 1/L with fixed large lambda) where lambda is the 't Hooft coupling and L is the number of Bethe momenta. The two limits do not commute apart from the leading term which reproduces the result obtained with the Arutyunov-Frolov-Staudacher phase …
Using considerations based on the thermodynamical Bethe ansatz as well representation theory of twisted Yangians we derive an exact expression for the overlaps between the Bethe eigenstates of the $SO(6)$ spin chain and matrix product states built from matrices whose commutators generate an irreducible representation of $\mathfrak{so}(5)$. The latter play the role of boundary states in a domain wall version of ${\cal N}=4$ SYM theory which has non-vanishing, $SO(5)$ symmetric vacuum expectation values on one side of a co-dimension one wall. This theory, which constitutes a defect CFT, is known…
We revisit the computation of the 2-loop correction to the energy of a folded spinning string in AdS_5 with an angular momentum J in S^5 in the scaling limit log S, J >>1 with J / log S fixed. This correction gives the third term in the strong-coupling expansion of the generalized scaling function. The computation, using the AdS light-cone gauge approach developed in our previous paper, is done by expanding the AdS_5 x S^5 superstring partition function near the generalized null cusp world surface associated to the spinning string solution. The result corrects and extends the previous conforma…
In this article we review the world-sheet scattering theory of strings on AdS 5 x S5. The asymptotic spectrum of this world-sheet theory contains both fundamental particles and bound states of the latter. We explicitly derive the S-matrix that describes scattering of arbitrary bound states. The key feature that enables this derivation is the so-called Yangian symmetry which is related to the centrally extended su(2|2) superalgebra. Subsequently, we study the universal algebraic properties of the found S-matrix. As in many integrable models, the S-matrix plays a key role in the determination of…
In this paper we find the Yangian algebra responsible for the integrability of the AdS2 X S2 X T^6 superstring in the planar limit. We demonstrate the symmetry of the corresponding exact S-matrix in the massive sector, including the presence of the secret symmetry. We give two alternative presentations of the Hopf algebra, along with related discussions on the issue of evaluation representations. We study the classical r-matrix, and re-discover the need for a secret symmetry also in this context. Finally, taking the simplifying zero-coupling limit of the S-matrix as a generating R-matrix for t…
We investigate the type IIA AdS(3) x S(3) x M(4) superstring with M(4)=S(3) x S(1) or M(4)=T(4). String theory in this background is interesting because of AdS3/CFT2 and its newly discovered integrable structures. We derive the kappa symmetry gauge-fixed Green-Schwarz string action to quadratic order in fermions and quartic order in fields utilizing a near BMN expansion. As a first consistency check of our results we show that the two point functions are one-loop finite in dimensional regularization. We then perform a Hamiltonian analysis where we compare the energy of string states with the p…
We apply the algebraic Bethe ansatz technique to compute the eigenvalues of the transfer matrix constructed from the general bound state S-matrix of the light-cone AdS5 x S5 superstring. This allows us to verify certain conjectures on the quantum characteristic function, and to extend them to the general case.
We study the bulk and boundary scattering of the sl(N) twisted Yangian spin chain via the solution of the Bethe ansatz equations in the thermodynamic limit. Explicit expressions for the scattering amplitudes are obtained and the factorization of the bulk scattering is shown. The issue of defects in twisted Yangians is also briefly discussed.
We present a classification of diagonal, antidiagonal and mixed reflection matrices related to Yangian and super-Yangian R matrices associated to the infinite series so(m), sp(n) and osp(m|n). We formulate the analytical Bethe Ansatz resolution for the so(m) and sp(n) open spin chains with boundary conditions described by the diagonal solutions.
This article reviews the application of integrability to the spectral problem of strings on AdS_5 x S^5 and its deformations. We begin with a pedagogical introduction to integrable field theories culminating in the description of their finite-volume spectra through the thermodynamic Bethe ansatz. Next, we apply these ideas to the AdS_5 x S^5 string and in later chapters discuss how to account for particular integrable deformations. Through the AdS/CFT correspondence this gives an exact description of anomalous scaling dimensions of single trace operators in planar N=4 supersymmetry Yang-Mills …
Bethe ansatz inside Calogero-Sutherland models
本研究利用Bethe ansatz和Yangian对称性研究三角量子自旋Calogero-Sutherland模型，构造新的守恒电荷并给出推广的本征基，同时综述了非均匀XXX链的Bethe ansatz方法。
We develop a new approach to Baxter Q-operators by relating them to the theory of Yangians, which are the simplest examples for quantum groups. Here we open up a new chapter in this theory and study certain degenerate solutions of the Yang-Baxter equation connected with harmonic oscillator algebras. These infinite-state solutions of the Yang-Baxter equation serve as elementary, "partonic" building blocks for other solutions via the standard fusion procedure. As a first example of the method we consider sl(n) compact spin chains and derive the full hierarchy of operatorial functional equations …
Inspired by the integrable structures appearing in weakly coupled planar N=4 super Yang-Mills theory, we study Q-operators and Yangian invariants of rational integrable spin chains. We review the quantum inverse scattering method along with the Yang-Baxter equation which is the key relation in this systematic approach to study integrable models. Our main interest concerns rational integrable spin chains and lattice models. We recall the relation among them and how they can be solved using Bethe ansatz methods incorporating so-called Q-functions. In order to remind the reader how the Yangian em…
We perform a detailed study of the type IIA superstring in AdS(4) x CP(3). After introducing suitable bosonic light-cone and fermionic kappa worldsheet gauges we derive the pure boson and fermion SU(2|2) x U(1) covariant light-cone Hamiltonian up to quartic order in fields. As a first application of our derivation we calculate energy shifts for string configurations in a closed fermionic subsector and successfully match these with a set of light-cone Bethe equations. We then turn to investigate the mismatch between the degrees of freedom of scattering states and oscillatory string modes. Since…
We consider superstrings on the pure-Ramond-Ramond $AdS_3\times S^3\times T^4$ background. Using the recently-proposed dressing factors for the worldsheet S matrix, we formulate the string hypothesis for the mirror Bethe-Yang equations, and use it to derive the canonical mirror thermodynamic Bethe ansatz (TBA) equations of the model. For the first time, these equations account for all massive and massless modes of the model, and do not resort to any limit or special kinematics. We also discuss the simplified mirror TBA equations and the Y-system of the model.
The Yangian level-one hypercharge generator for the super Wilson loop in N = 4 supersymmetric Yang-Mills theory is constructed. Moreover, evidence for the presence of a corresponding symmetry generator at all higher levels is provided. The derivation is restricted to the strong-coupling description of the super Wilson loop and based on the construction of novel conserved charges for type IIB superstrings on AdS_5 x S^5.
A strongly correlated electron system with controlled hopping, in the line of the recently proposed generalized Hubbard models as candidates for high T_c-superconductors, is considered. The model along with a whole class of such systems are shown to be completely integrable with explicit quantum R-matrices and the Lax operators. Inspite of novelties in the Bethe ansatz solution, the final results do not deviate much from those of the standard Hubbard model. However, the symmetry of the model is changed to a recently discovered twisted Yangian symmetry.
One-point functions in AdS/dCFT: MPS and twisted Yangian
本文研究 D5-D3 探针膜系统对偶缺陷场论中的标量单点函数，将其计算映射为矩阵乘积态与 Bethe 态的重叠，并证明矩阵乘积态满足扭曲边界 Yang-Baxter 方程，为探针膜系统及非平衡系统研究提供新方法。
Bethe ansatz equations for quantum $\mathcal{N}=2$ KdV systems
本研究基于对$\widehat{\mathfrak{gl}}(1|1)$仿射Yangian的前期研究，提出了适用于$\mathcal{N}=2$量子KdV系统能谱的Bethe ansatz方程，为该量子可积系统的能谱求解提供了新方法。
We formulate the Bethe Ansatz equations for the open super spin chain based on the super Yangian of osp(M|2n) and with diagonal boundary conditions. We then study the bulk and boundary scattering of the osp(1|2n) open spin chain.
Recently, it was demonstrated that one-loop energy shifts of spinning superstrings on AdS5xS5 agree with certain Bethe equations for quantum strings at small effective coupling. However, the string result required artificial regularization by zeta-function. Here we show that this matching is indeed correct up to fourth order in effective coupling; beyond, we find new contributions at odd powers. We show that these are reproduced by quantum corrections within the Bethe ansatz. They might also identify the "three-loop discrepancy" between string and gauge theory as an order-of-limits effect.
We identify certain blocks in the S-matrix describing the scattering of bound states of the AdS5 x S5 superstring that allow for a representation in terms of universal R-matrices of Yangian doubles. For these cases, we use the formulas for Drinfeld's second realization of the Yangian in arbitrary bound-state representations to obtain the explicit expressions for the corresponding R-matrices. We then show that these expressions perfectly match with the previously obtained S-matrix blocks.
We study the partition function of the six-vertex model in the rational limit on arbitrary Baxter lattices with reflecting boundary. Every such lattice is interpreted as an invariant of the twisted Yangian. This identification allows us to relate the partition function of the vertex model to the Bethe wave function of an open spin chain. We obtain the partition function in terms of creation operators on a reference state from the algebraic Bethe ansatz and as a sum of permutations and reflections from the coordinate Bethe ansatz.
We present a nested algebraic Bethe ansatz for one-dimensional open so(2n)- and sp(2n)-symmetric spin chains with diagonal boundary conditions and described by the extended twisted Yangian. We use a generalization of the Bethe ansatz introduced by De Vega and Karowski which allows us to relate the spectral problem of a so(2n)- or sp(2n)-symmetric open spin chain to that of a gl(n)-symmetric open spin chain. We explicitly derive the structure of Bethe vectors and the nested Bethe equations.
We continue the investigation of two-loop string corrections to the energy of a folded string with a spin S in AdS_5 and an angular momentum J in S^5, in the scaling limit of large J and S with ell=pi J/(lambda^(1/2) ln S)=fixed. We compute the generalized scaling function at two-loop order f_2(ell) both for small and large values of ell matching the predictions based on the asymptotic Bethe ansatz. In particular, in the small ell expansion, we derive an exact integral form for the ell-dependent coefficient of the Catalan's constant term in f_2(ell). Also, by resumming a certain subclass of mu…
We determine the S-matrix that describes scattering of arbitrary bound states in the light-cone string theory in AdS5 x S5. The corresponding construction relies on the Yangian symmetry and the superspace formalism for the bound state representations. The basic analytic structure supporting the S-matrix entries turns out to be the hypergeometric function 4F3. We show that for particular bound state numbers it reproduces all the scattering matrices previously obtained in the literature. Our findings should be relevant for the TBA and Luescher approaches to the finite-size spectral problem. They…
We study an integrable conformal OSp(2m + 2|2m) supercoset model as an analog to the AdS_5 X S^5 superstring world-sheet theory. Using the known S-matrix for this system, we obtain integral equations for states of large particle density in an SU(2) sector, which are exact in the sigma model coupling constant. As a check, we derive as a limit the general classical Bethe equation of Kazakov, Marshakov, Minahan, and Zarembo. There are two distinct quantum expansions around the well-studied classical limit, the lambda^{-1/2} effects and the 1/J effects. Our approach captures the first type, but no…
A quantum spin chain with non-conventional boundary conditions is studied. The distinct nature of these boundary conditions arises from the conversion of a soliton to an anti-soliton after being reflected to the boundary, hence the appellation soliton non-preserving boundary conditions. We focus on the simplest non-trivial case of this class of models based on the twisted Yangian quadratic algebra. Our computations are performed through the Bethe ansatz equations in the thermodynamic limit. We formulate a suitable quantization condition describing the scattering process and proceed with explic…
We discuss the possible extensions of Bethe/gauge correspondence to quantum integrable systems based on the super-Lie algebras of A type. Along the way we propose the analogues of Nakajima quiver varieties whose cohomology and K-theory should carry the representations of the corresponding Yangian and the quantum affine algebras, respectively. We end up with comments on the N=4 planar super-Yang-Mills theory in four dimensions.
In these proceedings we review the results of [1-3]. We show on the example of the SU(2) chiral-field how to reproduce the classical finite gap solutions for a large class of integrable sigma models from their exact quantum solutions. These solutions are usually formulated as Bethe ansatz equations for physical particles on a circle, with the interaction given by the factorized S-matrix conjectured from Zamolodchikovs' bootstrap procedure. Our method opens a new systematic way to justify this procedure. As an application of our method to the integrability in AdS/CFT correspondence, we reproduc…
We first analyse the integrable scattering theory describing the massless excitations of $AdS_2 \times S^2 \times T^6$ superstrings in the relativistic limit. The matrix part of the S-matrix is obtained in the BMN limit from the conjectured exact expression, and compared with known S-matrices with N=1 supersymmetry. A dressing factor, yet unknown for the complete theory, is here constructed based on relativistic crossing symmetry. We derive a Bethe-ansatz condition by employing a transfer-matrix technique based on the so-called free-fermion condition. This is known to overcome the problem of l…
In this thesis, we investigate hidden symmetries for the Maldacena-Wilson loop in N=4 super Yang-Mills theory, mainly focusing on its strong-coupling description as a minimal surface in $AdS_5$. In the discussion of the symmetry structure of the underlying string model, we highlight the role of the master symmetry which can be employed to construct all symmetries of the model. The algebra of these symmetries is worked out. For the concrete case of minimal surfaces in $AdS_5$, we discuss the deformation of the four-cusp solution, which provides the dual description of the four-gluon scattering …
We work out the algebraic Bethe ansatz for the worldsheet theory of the $AdS_3\times S^3\times T^4$ superstring, and use it to derive the transfer matrices for fundamental particles and bound states of the string and mirror model. We also show how the Bethe equations and transfer matrices are modified in the presence of an Abelian twist. These will be an important ingredient in the exploration of the mirror thermodynamic Bethe ansatz equations recently proposed by Frolov and Sfondrini, and their generalisation to twisted and deformed models.
We study the recently discovered q-deformed Poincare' supersymmetry of the AdS_3/CFT_2 integrable massless scattering, and demonstrate how the S-matrix is invariant under boosts. The boost generator has a non-local coproduct, which acts on the scattering matrix as a differential operator, annihilating it. We propose to reinterpret the boost action in terms of covariant derivatives on bundles, and derive an expression for the S-matrix as the path-ordered exponential of a flat connection. We provide a list of possible alternative interpretations of this emergent geometric picture, including a on…
An announcement of some results of a longer paper where the supersymmetric vacua of two dimensional N=2 susy gauge theories with matter are shown to be in one-to-one correspondence with the eigenstates of integrable spin chain Hamiltonians. The Heisenberg spin chain is mapped to the two dimensional U(N) theory with fundamental hypermultiplets, the XXZ spin chain is mapped to the analogous three dimensional super-Yang-Mills theory compactified on a circle, the XYZ spin chain and eight-vertex model are related to the four dimensional theory compactified on a torus. The correspondence extends to …
We derive the exact S-matrix for the scattering of particular representations of the centrally-extended psu(1|1)^2 Lie superalgebra, conjectured to be related to the massive modes of the light-cone gauge string theory on AdS_2 x S^2 x T^6. The S-matrix consists of two copies of a centrally-extended psu(1|1) invariant S-matrix and is in agreement with the tree-level result following from perturbation theory. Although the overall factor is left unfixed, the constraints following from crossing symmetry and unitarity are given. The scattering involves long representations of the symmetry algebra, …
We use AdS_5 x S^5 superstring sigma model perturbation theory to compute the leading one-loop corrections to the dispersion relations of the excitations near a long spinning string in AdS. This investigation is partially motivated by the OPE-based approach to the computation of the expectation value of null polygonal Wilson loops suggested in arXiv:1006.2788. Our results are in partial agreement with the recent asymptotic Bethe ansatz computation in arXiv:1010.5237. In particular, we find that the heaviest AdS mode (absent in the ABA approach) is stable and has a corrected one-loop dispersion…
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